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A generalized law of mixtures

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Abstract

The mechanical properties of two-phase composites are predicted using a rigorous continuum mechanics analysis and an equivalent microstructural transformation approach. This leads to a generalized law of mixtures which is contrasted with the classical linear law of mixtures which requires some explicit assumptions. The generalized law of mixtures enables prediction of a variety of mechanical properties of a two-phase composite with any volume fraction, grain shape and phase distribution. It is shown that the classical linear law of mixtures is a specific case of the generalized law of mixtures. Examples are given from continuous Cu-W composites, the particulate Co-WC system, Al/SiCp composites, α-β Ti-Mn alloys and α-β Cu-Zn alloys for the predictions of properties such as Young's modulus, yield strengths, flow stresses, the overall friction stresses and the overall Hall-Petch coefficients. It is shown that the theoretical predictions by the generalized law of mixtures are in very good agreement with the corresponding experimental results drawn from the literature, for both continuous fibre composites and particulate reinforced systems.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, The University of Surrey, GU2 5XH, Guildford, Surrey, UK

    Z. Fan, P. Tsakiropoulos & A. P. Miodownik

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  1. Z. Fan
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  2. P. Tsakiropoulos
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  3. A. P. Miodownik
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Fan, Z., Tsakiropoulos, P. & Miodownik, A.P. A generalized law of mixtures. JOURNAL OF MATERIALS SCIENCE 29, 141–150 (1994). https://doi.org/10.1007/BF00356585

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